If I understand correctly, the purpose of a jump function is to divide the continuum of starting points into known chunks so that parallel generators generate non-overlapping sequences of values, correct? For example, for 256-bits state generator, the jump (or long jump) create 128-bits (192-bits) chunks.
If I seed the (256-bits) generator with SplitMix using just one 64-bits number (generating 4 values with it), how well does it distribute the starting points of the generator? I mean, after how many steps at minimum would two parallel generators start to overlap?
On one hand, I would say that if the 64-bits seed "spreads" over 256-bits state, then it should be pretty well-spaced out, so for most practical usage it could be used instead of jump function as one would expect the starting points are pretty far apart. On the other hand, perhaps birthday paradox brings some two starting points too close to each other?
Thank you for any feedback!